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Reciprocal Formulae among Pell and Lucas Polynomials

Author

Listed:
  • Mei Bai

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Wenchang Chu

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
    Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

  • Dongwei Guo

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

Abstract

Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Lucas numbers.

Suggested Citation

  • Mei Bai & Wenchang Chu & Dongwei Guo, 2022. "Reciprocal Formulae among Pell and Lucas Polynomials," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2691-:d:875811
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    References listed on IDEAS

    as
    1. Waleed Mohamed Abd-Elhameed & Andreas N. Philippou & Nasr Anwer Zeyada, 2022. "Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals," Mathematics, MDPI, vol. 10(13), pages 1-18, July.
    2. Pavel Trojovský, 2019. "On the Sum of Reciprocal of Polynomial Applied to Higher Order Recurrences," Mathematics, MDPI, vol. 7(7), pages 1-7, July.
    Full references (including those not matched with items on IDEAS)

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